Effect of Stress on the Trigonal Splittings of $d^3$ Ions in Sapphire ($\alpha$-${\mathrm{Al}}_2$${\mathrm{O}}_3$)

We have measured the effect of uniaxial stress on the trigonal splittings of the ground (${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}$) state and the first excited (${}_{}{}^2{}_{}{}^{}E$) state of the ${\mathrm{}\left(3d\right)\mathrm{}}^3$ ions ${\mathrm{V}}^{2+}$, ${\mathrm{Cr}}^{3+}$, and ${\mathrm{Mn}}^{4+}$ in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$. We find that compression along the $c$ axis alters the ground-state splitting $2D$ by an amount which is almost independent of the ionic charge. The effect on the excited-state splitting $\Lambda$, on the other hand, varies markedly through the isoelectronic sequence, changing sign on going from ${\mathrm{Cr}}^{3+}$ to ${\mathrm{Mn}}^{4+}$. Previous work by Macfarlane has shown that $\Lambda$ depends primarily on the diagonal trigonal field parameter $v$, while $2D$ depends primarily on the off-diagonal parameter $v^{\prime }$. We tentatively suggest that our data show that in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, $v^{\prime }$ depends predominantly on long-range interactions, while $v$ depends more on the immediate environment of the chromophoric ion. Data are also given concerning the effect on the ${}_{}{}^2{}_{}{}^{}E$ splitting of stress perpendicular to the $c$ axis, and concerning the shift of the ${}_{}{}^2{}_{}{}^{}E$ level as a whole under stress.